Existence of knotted vortex structures in stationary solutions of the Euler equations
type: Item
instance of: scholarly article
title: Existence of knotted vortex structures in stationary solutions of the Euler equations
zbMATH Open document ID: 1402.35214
DOI: 10.4171/176-1/5
author: Alberto Enciso
author: Daniel Peralta-Salas
publication date: 2018-11-14T00:00:00Z
review text: Summary: In this paper, we review recent research on certain geometric aspects of the vortex lines of stationary ideal fluids. We mainly focus on the study of knotted and linked vortex lines and vortex tubes, which is a topic that can be traced back to Lord Kelvin and was popularized by the works of Arnold and Moffatt on topological hydrodynamics in the 1960s. In this context, we provide a leisurely introduction to some recent results concerning the existence of stationary solutions to the Euler equations in Euclidean space with a prescribed set of vortex lines and vortex tubes of arbitrarily complicated topology. The content of this paper overlaps substantially with the one the authors published in [the authors, Eur. Math. Soc. Newsl. 96, 26--33 (2015; Zbl 1321.35182)]. For the entire collection see [Zbl 1396.00017].
Mathematics Subject Classification ID: 35Q31
zbMATH DE Number: 6979382
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/176-1/5
OpenAlex ID: W4233204203
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description: scientific article; zbMATH DE number 6979382